Question

How do I solve the inequality 6|p|+8>-22? It's a multiple choice question on my homework and the answers available are either:
A) {All real numbers}
B) -5 < p < 5

Answer 1

$6|p|+8\ \textgreater \ -22$

Subtract 8.  $6|p|\ \textgreater \ -30$

Divide by 6.  $|p|\ \textgreater \ -5$

The solution set is all real numbers because no matter what number is chosen for p, its absolute value will be bigger than any negative number.

Answer 2

 6|p|+8 > - 22 ; could be written :
|6.p| + 8 > - 22. Now subtract 8 to both sides

|6p| +8 -8>-22 -8 → |6p|  > - 30 . Divide both sides by 6:

|p| > - 5
Clearing the absolute value bars yields:

p> - 5 and p< 5 (remember |x| = a → x = +a and x = -a)
Then :

- 5< p < +5

------------------------(-5)---------------------0--------------------(+5)----------------------
                               ∅============(P)============∅